Electronic quantum information probability transfer

ABSTRACT

Systems and methods for digital communication utilizing entangled qubits are disclosed. The disclosed systems and methods exploit selective entanglement swapping to transfer an entangled state between a sending device and a receiving device. Each device includes pairs of qubits that are independently entangled with pairs of qubits in the other device. By selectively entangling the qubits within a pair in the sending device, the qubits of the corresponding pair in the receiving device also are selectively entangled. When the qubits are entangled, they are projected onto a particular entangled state type. Though no information may be transferred through selective entanglement of one qubit pair, systems and methods of the present disclosure determine whether a set of pairs of qubits are entangled by determining whether the distribution of pairs is a correlated or uncorrelated distribution (a probabilistic approach) and transform the distribution type to a classical bit of data.

FIELD

The present disclosure relates to systems and methods for digitalcommunication utilizing entangled qubits.

BACKGROUND

Information may be communicated by conventional means such as electronicsignals, electromagnetic signals, photonic signals, audio signals, etc.For long distance and/or high-speed communication, typically some formof electronic communication is utilized, e.g., wired and/or wirelesselectrical, electromagnetic, and/or optical systems. Solutions typicallyrequire a physical communication channel (e.g., a wire, a fiber optic, awaveguide) and/or a clear path (a line of sight) between the sendingdevice and the receiving device. Some types of communication systems mayrely on an intense source that broadcasts a signal in a range ofdirections (e.g., a radio broadcast). All of these solutions arevulnerable to eavesdropping, jamming, and/or manipulation of thecommunication signal. Further, physical obstacles and/or distancebetween the sending device and the receiving device may hindercommunication, for example, by blocking the signal and/or reducing thesignal to noise ratio at the receiving device. Hence, there is a needfor secure and/or reliable communication systems and methods.

SUMMARY

Systems and methods for digital communication utilizing entangled qubitsare disclosed. The disclosed systems and methods exploit selectiveentanglement swapping to transfer an entangled state between a sendingdevice and a receiving device. Each device includes pairs of qubits thatare independently entangled with pairs of qubits in the other device. Byselectively entangling the qubits within a pair in the sending device,the qubits of the corresponding pair in the receiving device also areselectively entangled. When the qubits are entangled, they are projectedonto a particular entangled state type. Though no information may betransferred through selective entanglement of one qubit pair, systemsand methods of the present disclosure determine whether a set of pairsof qubits are entangled by determining whether the distribution of pairsis a correlated or uncorrelated distribution (a probabilistic approach)and transform the distribution type to a classical bit of data.

Methods may include digitally communicating between a sending device anda receiving device. In this example, each of the sending device and thereceiving device includes an entanglement set of entanglement pairs ofqubits. Each qubit of the sending device is entangled with acorresponding qubit of the receiving device. This method of digitallycommunicating includes sending a classical bit from the sending deviceto the receiving device by one of (a) entangling each entanglement pairof the entanglement set of the sending device to produce a correlateddistribution in the entanglement set of the sending device in whichevery entanglement pair of the entanglement set of the receiving deviceis entangled, or (b) entangling less than all of the entanglement pairsof the entanglement set of the sending device to produce an uncorrelateddistribution in the entanglement set of the receiving device in whichless than all entanglement pairs of the entanglement set of thereceiving device are entangled. The method also includes receiving theclassical bit at the receiving device from the sending device by one of(a) determining that each entanglement pair of the entanglement set ofthe receiving device is in a possible entangled state to identify thecorrelated distribution in the entanglement set of the receiving device,or (b) determining that at least one of the entanglement pairs of theentanglement set of the receiving device is in a separable state toidentify the uncorrelated distribution in the entanglement set of thereceiving device. The classical bit sent and received has one of twobinary values that correspond to the correlated distribution and theuncorrelated distribution.

An example of a method of digitally communicating between a sendingdevice and a receiving device is time synchronization between thesending device (which is at a sending location) and the receiving device(which is at a receiving location). This method includes polling by thereceiving device for a marker classical bit corresponding to acorrelated distribution by sequentially checking the entanglement setsof an entanglement queue of the receiving device at least untilidentifying the marker classical bit. For each entanglement set of theentanglement queue of the receiving device that is checked, the checkingincludes one of (a) determining that each entanglement pair of theentanglement set checked is in a possible entangled state to identifythe correlated distribution in the entanglement set checked and toidentify the marker classical bit, or (b) determining that at least one,optionally each, of the entanglement pairs of the entanglement setchecked is in a separable state to identify an uncorrelated distributionin the entanglement set checked. The method also includes sending fromthe sending device to the receiving device, at a predetermined localsend time during the polling, a bitstream of classical bits, eachclassical bit corresponding to the correlated distribution in one of theentanglement sets of an entanglement queue of the sending device, byentangling each entanglement pair of each entanglement set of theentanglement queue of the sending device to produce the correlateddistribution in each of the entanglement sets of the entanglement queueof the receiving device. The method also includes determining a timeoffset between the sending location and the receiving location bycomparing the local send time with a local receive time that correspondsto first receiving the marker classical bit at the receiving device.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of a communication system fordigital communication utilizing entangled qubits.

FIG. 2 is a schematic representation of an example of an entanglementdevice.

FIG. 3 is a schematic representation of another example of anentanglement device.

FIG. 4 is a schematic representation of the organization of entangledqubits within two communication devices.

FIG. 5 is a schematic representation of methods for digitalcommunication utilizing entangled qubits.

DESCRIPTION

FIGS. 1-5 illustrate systems and methods for digital (electronic)communication utilizing entangled qubits. In general, in the drawings,elements that are likely to be included in a given embodiment areillustrated in solid lines, while elements that are optional oralternatives are illustrated in dashed lines. However, elements that areillustrated in solid lines are not essential to all embodiments of thepresent disclosure, and an element shown in solid lines may be omittedfrom a particular embodiment without departing from the scope of thepresent disclosure. Elements that serve a similar, or at leastsubstantially similar, purpose are labeled with numbers consistent amongthe figures. Like numbers in each of the figures, and the correspondingelements, may not be discussed in detail herein with reference to eachof the figures. Similarly, all elements may not be labeled or shown ineach of the figures, but reference numerals associated therewith may beused for consistency. Elements, components, and/or features that arediscussed with reference to one or more of the figures may be includedin and/or used with any of the figures without departing from the scopeof the present disclosure.

FIG. 1 is a schematic representation of communication systems 10 fordigital communication that rely on entangled qubits 70. Communicationsystems 10 are configured to transfer one or more classical bits of databetween two or more communication devices 12. Each of the communicationdevices 12 may be a sending device 14 and/or a receiving device 16(e.g., may be configured to send classical bits or receive classicalbits). Each of the communication devices 12 include qubits 70 that areentangled with qubits 70 of one of the other communication device(s) 12.The entanglement of the qubits 70 is utilized to transmit a digitalmessage of classical bits between the communication devices 12. Themessage may be transmitted without any corresponding classicalcommunication. Additionally or alternatively, the communication devices12 may not be connected by any sort of classical communication channel(cable, radio link, free-space laser link, conveyance, transporter,etc.) and/or may not include any classical communication transmitterconfigured to communicate with other communication devices 12.

Communication systems 10 are configured to send and to receive classicalbits of data by selectively entangling qubits 70 in a sending device 14and determining whether the corresponding qubits 70 in a receivingdevice 16 are likely in an entangled state or an unentangled state (alsocalled a separable state). Sending devices 14 are configured toselectively entangle their qubits 70 to transmit classical bits of datawith values (e.g., 1 or 0) that correspond to the entangled state of thequbits 70 (e.g., a value of 1) or the unentangled state of the qubits 70(e.g., a value of 0). Receiving devices 16 are configured to determinewhether their qubits 70 are likely in an entangled state or anunentangled state to receive classical bits of data with values (e.g., 1or 0) corresponding to the entangled state determination (e.g., a valueof 1) or the unentangled state determination (e.g., a value of 0).

As used herein, classical refers to classical physics and systems thatmay be described by classical physics without resort to a quantumphysical description. A classical bit is a basic unit of informationthat may be one of two binary values, e.g., 0 or 1, + or −, true orfalse. A classical bit may encompass more than two values, for example 3(i.e., a trit), 4, 5, or more values.

Qubits 70, also called quantum bits, are basic units of quantuminformation. Qubits 70 are two-state quantum systems that may becharacterized as a superposition of the two states. The quantum systemmay be in a non-trivial superposition state in which both of the twostates are simultaneously occupied with a relative probability (alsocalled a probability amplitude) or in a trivial ‘superposition’ in whichonly one of the two states is occupied (analogous to a classical bit).

A superposition of states is a quantum property in which a quantumsystem simultaneously occupies all of the quantum states (e.g., the twostates) with a characteristic occupation coefficient (the probabilityamplitude) for each state. While the superposition of states isundisturbed, the quantum system may be considered to be in all states atonce. For example, a particle in a superposition of location states maybe characterized as in two places at once, or in an undeterminedlocation. However, when the quantum system is observed in a manner toestablish which quantum state is occupied, the superposition of statescollapses to one of the states of the quantum system (i.e., theprobability amplitudes are altered by the observation). For example, theparticle in a superposition of two locations would be actually observedto be in just one of the two locations. The probability of finding anyone particle of an ensemble of particles in identical superpositionstates is dictated by the superposition state (i.e., the occupationcoefficients/probability amplitudes). However, the actual state (e.g.,location) of any individual particle would not be known (would beundetermined) until observed (measured). An observation (measurement)may be said to project the quantum system into the observed (measured)state.

Mathematically, a superposition of states in a two-state system may beexpressed as:|Ψ>=α|0>+β|1>where the two states are |0> and |1>, the superposition state is |Ψ>,and the probabilities of measuring the quantum system in state |0> and|1> are |α²| and |β²|, respectively. The probability amplitudes a and β(which may be imaginary numbers) are normalized such that |+²|+|β²|=1.The two states, |0> and |1>, also may be referred to as basis states andmay be eigenstates of observables of the quantum system. Hence, asuperposition may be described as a linear combination of basis statesand/or a linear combination of eigenstates of observables of the quantumsystem.

Quantum systems may include a single quantum object or an ensemble ofquantum objects. Examples of quantum objects include photons, electrons,ions, atoms, molecules, quasiparticles, excitons, plasmons, and quantumdots. Quantum objects and/or quantum systems also may be referred to asparticles, even if the quantum object and/or quantum system is a photon,a quasiparticle, a composite object, etc. Quantum objects and/or quantumsystems may be bosons, fermions, and/or combinations of bosons andfermions.

The two states of qubits 70 are two quantum states of the quantum systemthat are distinguishable. For example, the states may be a ground stateand an excited state, Fock states (also called number states, e.g., thepresence and the absence of a particle), spin states (e.g., spin up andspin down), polarization states (e.g., horizontal and verticalpolarization, right circular polarization and left circularpolarization), linear momentum states, angular momentum states, orbitalangular momentum states, position states, energy-time states (e.g.,early and late states as used in time-bin encoding), and coherent states(e.g., an amplitude-squeezed state and a phase-squeezed state of light).Hence, qubits 70 may be based upon, for example, polarization of aphoton, orbital angular momentum of a photon, presence of a photon, spinof an electron, and/or presence of an electron.

Entanglement is a possible quantum property of a system of two or morequantum systems, each in a superposition of basis states, e.g., a systemof two or more qubits 70. When two quantum systems are entangled theyare said to be in an entangled state. Though each quantum system remainsin a superposition of basis states while entangled (and, hence, eachquantum system is in an undetermined state while entangled), measurementof one of the quantum systems (determining which is the basis state ofthe quantum system) also may uniquely determine the outcome of ameasurement on the other quantum system(s). One constituent of anentangled state cannot be fully described without considering theother(s). Like individual quantum systems, the state of an entangledsystem is expressible as a superposition of basis states, which may beeigenstates of some observable(s). Entanglement is severed (broken) whenthe entangled quantum systems decohere through interaction with theenvironment, for example, when a measurement is made.

In some entangled states, the individual quantum systems will always bedetermined to be in the same basis state (positively correlated). Insome entangled states, the individual quantum systems will always bedetermined to be in different basis states (anti-correlated, alsoreferred to as negatively correlated). For example, two electrons in ananti-correlated entangled spin state (both electrons equally likely tobe spin up or spin down) are entangled such that the electrons wouldalways be measured in opposite spin states (one spin up and one spindown), although the spin state of either individual electron wouldremain (individually) random (i.e., equally likely to be spin up or spindown).

Further, the basis states of the quantum systems generally are notunique. As examples, spin of an electron and polarization of a photonmay be measured relative to an arbitrary direction (perpendicular to thepath of travel). Spin up and spin down states relative to one axis(e.g., an x-axis) may be basis states (a basis set). Equally valid basisstates (another basis set) may be spin up and spin down states relativeto another axis (e.g., a z-axis oriented perpendicular to the x-axis).The correlation between the measurements of the entangled quantumsystems holds for all equivalent basis directions. If one entangledquantum system is measured in one basis direction (i.e., in one basisset), the other entangled quantum system(s) will be correlated in thesame basis direction (basis set). However, if the entangled quantumsystems are measured in different basis directions, the exactcorrelation is lost. Whatever the basis direction, the entangled quantumsystems will be exactly correlated in just that direction, as though thebasis direction of the measurement of one quantum system is communicatedto the other quantum system(s).

Entanglement links the entangled quantum systems such that the measuredstates of the entangled quantum systems are correlated, even when thequantum systems are physically separated by distances (and/or times)that would otherwise have no possible classical communication channel.Thus, the link between the entangled quantum systems may be said to bein the ‘elsewhere,’ the region of spacetime outside of the light cones(the region of possible causal connections) of either quantum system.And, entanglement may be described as a non-local property of the set ofentangled quantum systems, meaning that the separated entangled quantumsystems can influence each other.

Entanglement imposes a correlation on the measurements of entangledquantum systems even when the entangled quantum systems are measured‘simultaneously,’ i.e., faster than light could travel between theentangled quantum systems. Hence, entangled quantum systems may appearto communicate a measurement (e.g., the result and basis set) of one ofthe quantum systems to another of the quantum systems at super-luminalspeeds (i.e., essentially simultaneously despite being separated). Atleast in part because spatially-separated simultaneity is a relativephenomenon (different observers may see separated events occurringsimultaneously or at different times), entangled quantum systems mayappear to communicate from the future to the past. An alternative pointof view of the apparent transmission of signals from the future to thepast can be found in the concept of ‘counterfactual’ entanglement, see,e.g., Oliver Cohen, Phys. Rev. A, 60:1 Jul. 1999. As used herein,backward time propagation of signals (transmission of signals from thefuture to the past) is used to describe the same phenomenon. Analternative model may be substituted without loss of generality.

The entanglement link between entangled quantum systems may be severed(broken) by decoherence of the entangled state. Though the entangledstate may be decohered by interactions with the local environment of oneor more of the entangled quantum systems, the entanglement link is notgenerally influenced by the environment between the entangled quantumsystems like a classical communication channel would be. Specifically, aclassical communication channel transmits a signal between two locationsand the channel is subject to interference such as blocking oreavesdropping by manipulation of the environment (e.g., by severing thechannel or by adding a listening device). An entanglement link is notmanifest in any physical object but the entangled quantum systems, andthe entanglement link is not carried by any field between the entangledquantum systems. Thus, communication through an entanglement link wouldnot be blocked and/or intercepted by something in the space between theentangled particles. Because the communication through the entanglementlink may not be intercepted, secure communications are possible withoutresort to encryption. Because the communication through the entanglementlink may not be blocked, and because the distance between the entangledquantum systems does not degrade the entanglement link, entanglementlinks appear useful for satellite communication, communication without aline of sight, submerged submarine communication, undergroundcommunication (e.g., mining, spelunking), and transmission from aircraftblack boxes.

While entangled quantum systems appear to be well suited to secure,covert, and/or super-luminal communication, the no-communication theoremstates that measurement of one entangled quantum system of an entangledgroup of quantum systems communicates no information to the otherquantum system(s). That is, making a measurement of a subsystem (one ofthe entangled quantum systems) of the total system (the entangled groupof quantum systems) imparts no information to the rest of the totalsystem (i.e., is not detectable by the rest of the total system).

Though entanglement may involve two or more quantum systems, generaldiscussion throughout this disclosure may refer to entanglement of twoquantum systems for clarity. Hence, reference to two entangled quantumsystems (e.g., a pair of entangled qubits) is intended to include two ormore entangled quantum systems, e.g., two, three, four, or moreentangled quantum systems.

In an entangled state, the entangled quantum systems show non-classicalcorrelations between individual measurements on the individual quantumsystems, such as positive or negative correlations regardless of basisset. For an entangled system of two qubits 70, four maximally entangledstates exist (i.e., states with maximal entanglement correlations).These states are known as Bell states.

The four Bell states for a two qubit entangled system are:

$\left. \Phi^{+} \right\rangle = {\frac{1}{\sqrt{2}}\left\lbrack {\left. {0_{A}0_{B}} \right\rangle + \left. {1_{A}1_{B}} \right\rangle} \right\rbrack}$

$\begin{matrix}{\left. \Phi^{-} \right\rangle = {\frac{1}{\sqrt{2}}\left\lbrack {\left. {0_{A}0_{B}} \right\rangle - \left. {1_{A}1_{B}} \right\rangle} \right\rbrack}} \\{\left. \Psi^{+} \right\rangle = {\frac{1}{\sqrt{2}}\left\lbrack {\left. {0_{A}1_{B}} \right\rangle + \left. {1_{A}0_{B}} \right\rangle} \right\rbrack}} \\{\left. \Psi^{-} \right\rangle = {\frac{1}{\sqrt{2}}\left\lbrack {\left. {0_{A}1_{B}} \right\rangle - \left. {1_{A}0_{B}} \right\rangle} \right\rbrack}}\end{matrix}$where the subscripts A and B refer to the two entangled qubits. Eachqubit (A and B) may be in one of two states, |0> and |1>, with equalprobability. In the |Φ⁺> and |Φ⁻> states, the two qubits will always bemeasured in the same state with equal probabilities of the two possibleoutcomes, i.e., both |0> or both |1> (expressed as |0_(A)0_(B)> and|1_(A)1_(B)>, respectively, in the Bell state equations). In the |Ψ⁺>and |Ψ⁻> states, the two qubits will always be measured in oppositestates with equal probabilities of the two possible outcomes, one |0>and one |1>, or the reverse (expressed as |0_(A)1_(B)> and |1_(A)0_(B)>in the Bell state equations). Thus, though each qubit independentlyappears to be randomly distributed between its basis states, |0> and|1>, the combined measurement of the two qubits always shows acorrelation. The states |Φ⁺> and |Φ⁻> have a positive correlation andthe states |Ψ⁺> and |Ψ⁻> have a negative correlation. The states |Φ⁺>,|Φ⁻>, and |Ψ⁺> are all invariant upon swapping of qubits A and B, andtogether may be referred to as triplet states. The state |Ψ⁻> is notinvariant to the swap of qubits A and B, and may be referred to as thesinglet state.

Entanglement is the result of quantum systems interacting in aparticular fashion to link the states of each of the quantum systems.Entanglement may be the result of joint production of the quantumsystems, joint interaction of the quantum systems, and/or entanglementswapping (involving a joint measurement of related quantum systems).

Joint production of entangled quantum systems may be performed in anysuitable manner. As an example, subatomic particles may decay into anentangled pair of daughter particles. The decay may obey conservationlaws such as conservation of mass, energy, momentum, angular momentum,etc. Thus, the daughter particles may be produced such that total valueof the conserved quantity is known but the individual values of thedaughter particles is undetermined (i.e., the daughter particles may beformed in superposition states that are entangled with each other).Additionally, daughter particles may be formed at the same time(energy-time entanglement). For instance, a spin-zero particle may decayinto a pair of spin-½ particles. If angular momentum is conserved, thetotal spin remains zero after the decay and the daughter particles musthave opposite spins (an anti-correlated entangled state). As anotherexample, entangled photons may be produced through a process known asspontaneous parametric down conversion (also known as SPDC, parametricfluorescence, and parametric scattering). In SPDC, interaction of onephoton with a particular type of non-linear crystal (such as BBO(beta-barium borate) crystal and a KDP (potassium dihydrogen phosphate)crystal results in two photons that have combined energies and momentaequal to the energy and momentum of the original photon and that havecorrelated polarizations. Additionally, the SPDC photons are formed atthe same time (energy-time entanglement). SPDC devices are known tothose skilled in the art and may be configured to emit entangled photonsthat share the same polarization (type I devices) or that haveperpendicular polarizations (type II devices). Type I devices produce apositive correlation and type II devices produce a negative correlation.

Entanglement through joint interaction of quantum systems may beperformed in any suitable manner. As an example, indistinguishablephotons impinging on a 50:50 beam splitter from opposite sides willemerge in a joint state emanating in one of two directions from the beamsplitter (the Hong-Ou-Mandel effect). Other methods include confiningphotons in a waveguide, atomic cascades, Raman scattering (between aphoton and an ion or atom), interactions in QED (quantum electrodynamic)cavities (which may entangle photons, ions, and/or atoms).

Entanglement swapping, another method of creating entanglement, relieson groups of previously entangled quantum systems. In entanglementswapping, one part of each of the groups of entangled quantum systems isentangled to entangle the other parts of the groups of entangled quantumsystems. Each entangled group includes at least two entangled quantumsystems, but, for clarity, entangled groups of two are discussed in thisexample. Similarly, entanglement swapping may be performed with morethan two entangled groups, but this example focuses on entanglementswapping with a pair of entangled groups.

Initially, each of the entangled groups has no correlation with theother, i.e., is independent of the other. The quantum systems of one ofthe entangled groups may have never interacted with the quantum systemsof the other entangled group. For the sake of this example, the quantumsystems of the first entangled group are called A1 and B1, and thequantum systems of the second entangled group are called A2 and B2. Theentangled groups may be split such that a first location may include onequantum system from each entangled group (i.e., A1 and A2) and a secondlocation may include the other quantum systems (i.e., B1 and B2). Thequantum systems at the first location (A1 and A2) may be entangled (asdiscussed herein with respect to entangling quantum systems) andobserved in the new entangled state (together referred to as a jointentanglement measurement). The joint entanglement measurement projectsthe quantum systems of the first location (A1 and A2) into an entangledstate and collapses the original entanglement within the entangledgroups (i.e., A1 and B1 are no longer entangled, and A2 and B2 are nolonger entangled). The joint entanglement measurement also projects thequantum systems of the second location (B1 and B2) into an entangledstate (typically, the same entangled state as that of A1 and A2), eventhough the quantum systems of the second location (B1 and B2) may neverhave directly interacted.

The joint entanglement measurement may be a Bell-state measurement,i.e., a measurement configured to project the quantum systems into atleast one of the Bell states. Some Bell-state measurements areconfigured to project the quantum systems into any of the Bell states(i.e., capable of measuring all Bell states), while other Bell-statemeasurements are configured to project the quantum systems into any of asubset of the Bell states (i.e., capable of measuring only some of theBell states). A Bell-state measurement, like a joint entanglementmeasurement, is an entangling operation.

FIG. 2 shows an example of a Bell-state measurement apparatus (which maybe, or may be a component of, an entanglement device 40 as discussedfurther herein). In this example, the qubits 70 are photons that may beentangled in polarization. The two qubits 70 initially travel alongseparate optical paths 50 a and 50 b. The two qubits 70 are directed(e.g., with conventional optics) to combine at a beam splitter 44 in theHong-Ou-Mandel configuration. The beam splitter 44 is configured totransmit and reflect a photon with equal probabilities, regardless ofthe initial polarization of the photon. The two qubits 70 may emergefrom the beam splitter in some combination of the optical paths 50 c and50 d.

At the terminuses of the optical paths 50 c and 50 d are a group ofdetectors 48 configured to measure the presence and polarization of thephoton(s) in the optical paths 50 c and 50 d. The detectors 48 arephotodetectors, generally configured for coincidence counting ofincoming photons. Examples of suitable detectors include avalanchephotodiodes and photomultiplier tubes. Prior to the detectors 48, eachoptical path 50 c and 50 d includes a polarizing beam splitter 46. Thepolarizing beam splitters 46 are each configured to transmit photons ofone polarization and reflect photons of the orthogonal polarization.Generally, the polarizing beam splitters 46 may be aligned such thathorizontal polarization is transmitted and vertical polarization isreflected. If a photon in an equal superposition of horizontal andvertical polarization states (more generally, in a superposition ofpolarization basis states that are aligned with the polarizing beamsplitter 46), the photon will be transmitted or reflected with equalprobabilities. The detectors 48 are each configured to measure one ofthe possible polarization directions along one of the optical paths 50 cand 50 d. Further, the detectors 48 may be configured for coincidencedetection such that the Bell-state measurement is performed only if twoof the detectors 48 detect a photon at essentially the same time.Additionally or alternatively, the detectors 48 may be configured todetect the number of photons (e.g., 1 or 2) that arrive.

The example Bell-state measurement apparatus of FIG. 2 may only uniquelydetermine two of the four Bell states unless the detectors 48 areconfigured to detect the number of photons also. With detectors 48configured to measure the presence or absence of photons (e.g.,configured in photon counting mode), this Bell-state measurementapparatus may uniquely detect the |Ψ⁺> and |Ψ⁻> Bell states. The |Φ⁺>and |Φ⁻> Bell states result in two photons simultaneously arriving inone of the detectors 48.

Ultimately, not all Bell states for entanglement in a single qubitvariable (e.g., polarization states) may be simultaneously detectablewith linear optical techniques. Hence, with linear optical techniques,at least one Bell state is indistinguishable from another. Thecorresponding Bell-state measurement may be said to be incomplete (i.e.,it is an incomplete Bell-state measurement). If a Bell-state measurementis ambiguous or fails (e.g., due to an incomplete Bell-state measurementor due to one or more of the photons not being detected), the qubits 70subject to the Bell-state measurement may not be entangled and/or may beentangled in a superposition of Bell states. Any correspondingentanglement swapping also may fail, be incomplete, and/or be ambiguous.

However, when qubits 70 are entangled in multiple qubit variables (e.g.,for photons, at least two of polarization states, energy-time states,orbital angular momentum states, and Fock states), the ‘extra’ qubitvariables may be exploited to measure all four Bell states of one of thequbit variables with linear optical techniques. Qubits 70 entangled inmultiple qubit variables may be called hyper-entangled qubits 70. ABell-state measurement configured to measure any of the four Bell-statesof one qubit variable may be said to be complete (i.e., it is a completeBell-state measurement).

FIG. 3 shows an example of a complete Bell-state measurement apparatusconfigured to determine the polarization Bell-state of photonshyper-entangled in polarization states and energy-time states. Manyprocesses create qubits 70 entangled in energy-time states, for example,processes that generate indistinguishable entangled qubits 70 at thesame time entangle those qubits 70 in time as well. Particles generatedat other times would not be entangled with the entangled qubits 70. Forphotons, detection time may be highly correlated to time of production(e.g., the optical path from source to detector may be known). Photonsgenerated by SPDC are energy-time entangled as well as polarizationentangled.

The optical paths 50 of the Bell-state measurement apparatus of FIG. 3begin like those in FIG. 2. The two qubits 70 are directed to andthrough a beam splitter 44 in a Hong-Ou-Mandel configuration. After thebeam splitter 44, the qubits 70 of the |Ψ⁺> state will split between theupper and lower optical paths 50 and may be distinguished by detecting aphoton from each of the upper and lower optical paths 50 (e.g.,determining that one of the upper detectors 48 and one of the lowerdetectors 48 senses a photon). The qubits 70 of the other three Bellstates, |Ψ⁻>, |Φ⁺>, and |Φ⁻> travel together in one of the upper orlower optical paths 50.

The qubits 70 of the |Ψ⁻> state have orthogonal polarizations. One ofthe orthogonal polarizations is subject to a delay in a polarizationdelay device 52. In the polarization delay device 52, a polarizing beamsplitter 46 separates the horizontal and vertical polarizations into ashort path (e.g., horizontal polarization) and a long path (e.g.,vertical polarization). The short and long paths are then recombined ata second polarizing beam splitter 46. Which polarizations traverse theshort and long paths may be exchanged (e.g., horizontal polarizationcould be directed along the long path). The long path is illustrated asa pair of mirrors 54 in a trombone arrangement. Other types of opticaldelay lines may be used (e.g., a fiber optic). After traversing thepolarization delay device 52, the photons of the |Ψ⁻> state areseparated in time by a characteristic delay time and may bedistinguished by detecting a pair of photons with this characteristicdelay.

The qubits 70 of the |Φ⁺> and |Φ⁻> states are in superpositions ofidentical polarizations, with only phase differentiating the states(i.e., the sign in the superposition sum). Because the polarizations areidentical, the polarization delay device 52 does not separate the qubits70 of the |Φ⁺> and |Φ⁻> states. The output of the polarization delaydevices 52 leads to a polarization rotator 56 (also called acompensator) configured to rotate the polarization of incoming light45°. The polarization rotator 56 may be a half waveplate oriented torotate the incoming polarization by 45° (e.g., oriented at 22.5° to thevertical). The polarization rotator 56 effects a rotation of the basisset of the downstream detectors 48. The detectors 48 are configured todetect photons polarized in the +45°, −45° basis rather than thehorizontal, vertical basis. This rotation of basis may change the |Φ⁺>and |Φ⁻> states to:

$\begin{matrix}{\left. \Phi^{+} \right\rangle = {\frac{1}{\sqrt{2}}\left\lbrack {\left. {{{+ 45}{^\circ}},{{+ 45}{^\circ}}} \right\rangle + \left. {{{- 45}{^\circ}},{{- 45}{^\circ}}} \right\rangle} \right\rbrack}} \\{\left. \Phi^{-} \right\rangle = {\frac{1}{\sqrt{2}}\left\lbrack {\left. {{{+ 45}{^\circ}},{{- 45}{^\circ}}} \right\rangle + \left. {{{- 45}{^\circ}},{{+ 45}{^\circ}}} \right\rangle} \right\rbrack}}\end{matrix}$Therefore, the |Φ⁺> state may be distinguished by detecting a pair ofsimultaneous photons with the same polarization (in the +45°, −45°basis) along the same optical path 50 (upper or lower), and the |Φ⁻>state may be distinguished by detecting a pair of simultaneous photonswith orthogonal polarizations (in the +45°, −45° basis) along the sameoptical path 50 (upper or lower).

Returning to FIG. 1, communication systems 10 exploit the phenomenon ofentanglement swapping to transfer entangled states from the qubits 70 ofthe sending device 14 to the qubits 70 of the receiving device 16.

To leverage the entanglement swapping to transmit classical bits, thequbits 70 are entangled and organized as illustrated in FIG. 5. First,qubits 70 are entangled in entangled groups 72. The entangled groups 72include two or more qubits 70 in an entangled state. All qubits 70 of anentangled group 72 may be the same type (e.g., all photons) or differenttypes (e.g., a photon and an atom). Entangled groups 72 may behyper-entangled.

Each of the entangled groups 72 is partitioned among the communicationdevices 12 (e.g., half to the sending device 14 and half to thereceiving device 16), with each communication device including at leastone qubit 70 from each of the entangled groups 72. The communicationdevices 12 may be separated in different locations, designated Alice andBob, in keeping with the conventions of quantum information theory.Though FIG. 5 associates Alice with the sending device 14 and Bob withthe receiving device 16, the roles and devices of Alice and Bob may besymmetric and/or interchangeable. Hence, each of Alice and Bob may havea sending device 14, a receiving device 16, and/or a communicationdevice 12 configured for both sending and receiving, so long as at leastone of Alice and Bob has a sending device 14 and the other has areceiving device 16. Also, though just Alice and Bob may be referenced,the number of sites and/or devices may be greater than two. Inembodiments with two or more sites, each site and/or device may beconfigured to communicate directly with one or more of the other sites.

Entangled states may be delicate and subject to rapid decoherence (lossof entanglement). As examples of relatively robust entangled states,certain quantum systems have been entangled for minutes and entangledphotons have propagated over 100 km (kilometers). Communication devices12 may be configured to protect the entangled states of the entangledgroups 72 and/or to utilize the entangled groups 72 before thecorresponding entangled states are likely to decohere.

Entangled qubits 70 based on photons generally decohere rapidly duringpropagation in the atmosphere, resulting in loss of entanglement withthe other entangled qubits 70 (e.g., a photon or an atomic system).Coherent photon states, e.g., as usually generated in a laser, are muchmore robust to decoherence. Hence, qubits 70 may include coherent photonstates. Propagation in space, a vacuum, or a waveguide typically doesnot lead to as rapid decoherence as propagation in the atmosphere.Therefore, communication devices 12 may be configured to propagatephotonic qubits 70 in space, a vacuum, and/or a waveguide to maintaincoherence of the entangled state of photonic qubits 70.

For entangled qubits 70 based upon ions and/or atoms, communicationsdevices 12 may include ion traps (e.g., a Paul trap) and/or atomic traps(e.g., a magnetic trap) configured to maintain coherence of theentangled state of ionic and/or atomic qubits 70.

Within each communication device 12, the separated, entangled qubits 70are arranged in pairs, called entanglement pairs 76. Each entanglementpair 76 of one communication device 12 has a corresponding entanglementpair 76 in the other communication device(s) 12. Thus, entanglement ofthe entanglement pair 76 of one communication device 12 (e.g., thesending device 14) results in entanglement of the correspondingentanglement pair 76 of the other communication device(s) (e.g., thereceiving device 16) via the mechanism of entanglement swapping.

As an example following the notations in FIG. 5, the communicationsystem 10 includes at least two entangled groups 72 of qubits 70. Thequbits 70 of the first entangled group 72 are designated A₁ and B₁. Thequbits 70 of the second entangled group 72 are designated A₂ and B₂. Thequbits 70 with the same index, e.g., A_(i) and B_(i), form independententangled groups 72. Each entangled group 72 is split between thesending device 14 and the receiving device 16, with one of the qubits 70of each entangled group 72 at each communication device 12.Specifically, the sending device 14 includes A₁ and A₂, and thereceiving device 16 includes B₁ and B₂. The separated, entangled qubits70 are arranged into corresponding entanglement pairs 76 in eachcommunication device 12. Specifically, the entanglement pair 76 of thesending device 14 is A₁ and A₂, and the corresponding entanglement pair76 of the receiving device 16 is B₁ and B₂.

Each of the entanglement pairs 76 are distinguishable (e.g., in anordered list, labelled, offset in time, and/or located in differentpositions). Each of the qubits 70 also may be distinguishable.

Within each communication device 12, the entanglement pairs 76 arearranged in one or more entanglement sets 80. Each entanglement set 80of one communication device 12 has a corresponding entanglement set 80in the other communication device(s) 12. Each entanglement pair 76 ofeach entanglement set 80 of each communication device 12 has acorresponding entanglement pair 76 in the corresponding entanglement set80 of the other communication device(s) 12. Thus, independententanglement of each of the entanglement pairs 76 of one entanglementset 80 of one communication device 12 (e.g., the sending device 14)results in the corresponding entanglement set(s) 80 of the othercommunication device(s) 12 (e.g., the receiving device 16) containingcorresponding entangled entanglement pairs 76.

Entanglement sets 80 correspond to classical bits as discussed furtherherein. All corresponding entanglement sets 80 in communication devices12 include the same number of entanglement pairs 76. However, eachentanglement set 80 within a communication device 12 may include anindependent number of entanglement pairs 76. Thus, some classical bitsmay be derived from a larger number of entanglement pairs 76 than otherclassical bits.

Following the example of FIG. 5, the sending device 14 includes at leasttwo entanglement pairs 76 arranged in an entanglement set 80. Thereceiving device 16 includes the same number of entanglement pairs 76arranged in the same manner in a corresponding entanglement set 80. Thefirst entanglement pair 76 of the sending device 14 includes the qubits70 designated A₁ and A₂. Other entanglement pairs 76 of the sendingdevice 14 may be designated as A_(2i-1) and A_(2i), where i is the indexof the entanglement pair 76. The last entanglement pair 76 of theindicated entanglement set 80 of the sending device 14 includes thequbits 70 designated as A_(2n-1) and A_(2n), where n is the total numberof entanglement pairs 76 in the entanglement set 80.

The receiving device 16 includes a first entanglement pair 76 of qubits70, B₁ and B₂. Other entanglement pairs 76 of the receiving device 16may be designated as B_(2i-1) and B_(2i), in analog to the correspondingqubits 70 of the sending device 14. The last entanglement pair 76 of theindicated entanglement set 80 of the receiving device 16 includes thequbits 70 designated as B_(2n-1) and B_(2n).

Within each communication device 12, the entanglement sets 80 areordered in an entanglement queue 84. The entanglement queues 84 of thecommunication devices 12 all have the same order. Communication devices12 are configured to utilize corresponding entanglement sets 80 in apredefined order (i.e., the order of the entanglement queues 84).

Communication devices 12 are configured to operate on at least oneentanglement pair 76 at a time. For example, communication devices 12may operate on, within one time period, one entanglement pair 76, twoentanglement pairs 76, one entanglement set 80, etc. Entanglement pairs76 may be generated as needed and/or communication devices 12 may beconfigured to store entanglement pairs 76 until the entanglement pair 76is needed to transmit a classical bit. Hence, entanglement queues 84 maybe replenished as entanglement pairs 76 and/or entanglement sets 80 areutilized (due to measurement of one of the underlying entangled groups72) and/or expire (due to actual or projected decoherence of theunderlying entangled groups 72).

Returning to FIG. 1, communication systems 10 may include an entangledqubit source 42 that is configured to produce entangled groups 72 andthat may be configured to produce entangled qubits 70 as discussedherein (e.g., by joint production, by joint interaction, and/or byentanglement swapping). The entangled qubit source 42 is configured toproduce independent entangled groups 72, meaning that qubits 70 of oneentangled group 72 are not produced entangled with qubits 70 of anotherentangled group 72.

The entangled groups 72 of the entangled qubit source 42 are split intoat least two pools, one for each communication device 12 (e.g., one forthe sending device 14 and one for the receiving device 16). In each poolis one qubit 70 from each of the entangled groups 72. A single pool maycorrespond to, and/or may be, a single entangled qubit 70 of anentangled group 72, one or more entanglement pairs 76, one or moreentanglement sets 80, and/or an entanglement queue 84.

The entangled qubit source 42 may be configured to transmit the pools tothe communication devices 12 (generally one pool for each communicationdevice 12). Additionally or alternatively, the entangled qubit source 42may be a component of one of the communication devices 12. Thatcommunication device 12 and/or the entangled qubit source 42 may beconfigured to transmit one of the pools of entangled qubits 70 to eachof the other communication devices 12.

Sending devices 14 are configured to selectively entangle selectedqubits 70 of the sending device 14. Sending devices 14 may be configuredto selectively entangle or not entangle the selected qubits 70 of thesending device 14.

Sending devices 14 include an entanglement device 40 configured toselectively entangle the qubits 70 of an entanglement pair 76 of thesending device 14. The entanglement device 40 may be configured toperform a joint entanglement measurement (e.g., a Bell-state measurementand/or a complete Bell-state measurement) to entangle the qubits 70. Theentanglement device 40 may be configured to selectively entangle one ormore entanglement pairs 76 at one time and/or one or more entanglementsets 80 at one time. Where the entanglement device 40 is configured toselectively entangle more than one entanglement pair 76 at the sametime, each entanglement pair 76 is entangled (or not) independently.

To not entangle selected entanglement pairs 76, sending devices 14 maybe configured to selectively discard one or both of the qubits 70 of theentanglement pair 76 and/or to selectively perform a separable-statemeasurement on one or both of the qubits 70 of the entanglement pair 76.A separable-state measurement is a measurement to determine theindividual states of the selected qubits 70, without entangling thequbits 70. Performing a separable-state measurement projects a separablestate (an unentangled state) onto the measured qubits 70. As an example,for qubits 70 based on the polarization of photons, a separable-statemeasurement may be performed by measuring the polarization (e.g.,determining a horizontal or vertical polarization) of each photonindependently.

Receiving devices 16 are configured to selectively determine whetherentanglement pairs 76 of entanglement sets 80 of the receiving device 16are likely entangled (due to entanglement of all of the correspondingentanglement pairs 76 of the sending device 14). Receiving devices 16include a measurement device 60 configured to measure the state of theentanglement pairs 76 of the selected entanglement set(s) 80.Measurement devices 60 may be configured to perform a separable-statemeasurement on each of the entanglement pairs 76 of the selectedentanglement set(s) 80.

Receiving devices 16 may be configured to determine whether theentanglement pairs 76 of the selected entanglement set 80 are in acorrelated distribution or in an uncorrelated distribution as discussedfurther herein. Further, receiving devices 16 may be configured toassign a classical bit value according to the type of distributiondetermined (e.g., a value of 1 for a correlated distribution and a valueof 0 for an uncorrelated distribution).

FIG. 5 schematically represents methods 100 of digital communicationutilizing entangled qubits. The foundation for the systems and methodsfor digital communication utilizing entangled qubits is at least tworelated entanglement pairs 76 located in at least two sites. As withFIG. 4, the two sites and the corresponding actors at those sites may belabelled Alice and Bob. Though generally Alice is described as thesender of information and Bob is described as the receiver, either orboth of Alice and Bob may send and/or receive information, so long as atleast one of Alice and Bob sends information and the other receivesinformation.

Methods 100 may include forming 106 an entanglement set 80 of at leasttwo entanglement pairs 76 and a corresponding entanglement set 80 of atleast two corresponding entanglement pairs 76. Each entanglement pair 76and corresponding entanglement pair 76 is formed together by firstforming a first entangled group 72 (by entangling two or more qubits 70)and a second entangled group 72 (by entangling two or more qubits 70)and then separating the qubits of first entangled group and the qubitsof the second entangled group to locate one qubit of each of the firstentangled group and the second entangled group in a first location(Alice) and to locate the other qubits of each of the first entangledgroup and the second entangled group in a second location (Bob). Thequbits in the first location (Alice) are the entanglement pair and thequbits in the second location (Bob) are the corresponding entangledpair.

Entangled groups 72 may be prepared in a known entanglement state. Forclarity, an example entangled group 72 may consist of identical qubitsAi, Bi, . . . , where i denotes the index of the entangled group. Afterentanglement, the qubits 70 of an entangled group 72 are separated andlocated at different sites, e.g., the Ai qubits are sent to Alice andthe Bi qubits are sent to Bob. The qubits 70 of entangled groups 72 arecollected into entanglement pairs 76, i.e., pairs of entangled qubits ateach location, each pair including one part of each of the twoconstituent entangled groups 72. For example, an entanglement pair withAlice may include qubits A1 and A2, and the corresponding entanglementpair with Bob may include qubits B1 and B2.

Methods 100 may include sending 102 a classical bit from the firstlocation (Alice) to the second location (Bob) by selectively entanglingall entanglement pairs 76 of an entanglement set 80 corresponding to theclassical bit. Selectively entangling includes one of (a) entanglingeach entanglement pair 76 of the entanglement set 80 (Alice'sentanglement set) to produce a correlated distribution in thecorresponding entanglement set 80 (Bob's entanglement set) in whichevery corresponding entanglement pair 76 of the correspondingentanglement set 80 is entangled, or (b) entangling less than all(optionally none) of the entanglement pairs 76 of the entanglement set80 (Alice's entanglement set) to produce an uncorrelated distribution inthe corresponding entanglement set 80 (Bob's entanglement set) in whichless than all (optionally none) of the corresponding entanglement pairs76 of the corresponding entanglement set 80 are entangled. The value ofthe transmitted classical bit (e.g., 1 or 0) corresponds to thecorrelated distribution (e.g., a value of 1) and the uncorrelateddistribution (e.g., a value of 0).

Methods 100 may include receiving 104 a classical bit from the firstlocation (Alice) at the second location (Bob) by determining the type ofdistribution in the corresponding entanglement set 80 (either acorrelated distribution or an uncorrelated distribution of correspondingentanglement pairs 76). Determining the distribution type includes oneof (a) determining that each corresponding entanglement pair 76 of thecorresponding entanglement set 80 (Bob's entanglement set) is in apossible entangled state to identify a correlated distribution in thecorresponding entanglement set 80 (Bob's entanglement set), or (b)determining that at least one of the corresponding entanglement pairs 76of the corresponding entanglement set 80 (Bob's entanglement set) is ina separable state to identify an uncorrelated distribution in thecorresponding entanglement set 80 (Bob's entanglement set). The value ofthe transmitted classical bit (e.g., 1 or 0) corresponds to thecorrelated distribution (e.g., a value of 1) and the uncorrelateddistribution (e.g., a value of 0).

Initially (before utilization of the entanglement pairs 76), theentangled groups 72 are entangled but the different qubits 70 of theentanglement pairs 76 are in separable states (unentangled with eachother). That is, entanglement exists only within each entangled group 72of an entanglement pair 76. To send a message, Alice may selectivelyentangle her qubits A1 and A2 of an entanglement pair (via selectiveutilization of an entanglement operation such as a Bell-statemeasurement). Through the process of entanglement swapping, once thequbits A1 and A2 are entangled, the corresponding qubits B1 and B2 ofBob's corresponding entanglement pair become likewise entangled, and theoriginal entanglements within the entangled groups (between A1 and B1,and between A2 and B2) are severed. After Alice has acted on her qubits(A1 and A2), Bob determines whether his qubits (B1 and B2) may beentangled by measuring correlations between his qubits. If Aliceentangled her qubits (A1 and A2), Bob's qubits (B1 and B2) would have astatistical correlation according to the entanglement state imposed byAlice (and optionally the original entanglement state(s) of theentangled groups). If Alice did not entangle her qubits (A1 and A2),Bob's qubits (B1 and B2) would remain in a separable state andmeasurements of Bob's qubits would be uncorrelated (random).

Without more, Bob cannot learn whether Alice entangled her qubits (A1and A2) by measuring his qubits (B1 and B2), consistent with theno-communication theorem. First, Bob would essentially observe hisqubits in an uncorrelated state if he did not measure his qubits withthe same basis set that Alice used to entangle her qubits. Therefore,Alice and Bob should arrange to entangle and to measure with a commonbasis set (e.g., along a common basis direction). Second, differententangled states impose different correlations on the constituent qubitsof Bob's entanglement pair. Measuring Bob's qubits in the same oropposite basis states does not imply any correlation unless Bob knowswhich type of entanglement state was applied by Alice (and optionallythe original entanglement state(s) of the constituent entangled groups).Third, if Alice selects to not entangle her qubits, Bob's qubits wouldbe in a separable state, with each possible measurement outcome random.Hence, even if Bob knows the basis set and the type of entanglement,Bob's qubits may be measured in a state consistent with the entanglementcorrelation despite the fact that Alice did not entangle her qubits. Forexample, if Alice entangles her qubits (A1 and A2) to impose ananti-correlated entangled state, the probability that Bob would measurehis qubits (B1 and B2) in opposite basis states (|0> and |1>, or |1> and|0>) is 50% each (as detailed in Table 1). If Alice does not entangleher qubits (A1 and A2), the probability that Bob would measure hisqubits (B1 and B2) in any pair of basis states (|0> and |0>, |0> and|1>, |1> and |0>, or |1> and |1>) is 25% (as detailed in Table 2).Therefore, if Bob measures his qubits in the |0> and |1> states, he doesnot know whether or not Alice entangled her qubits, as a measurement of|0> and |1> is consistent with either scenario.

TABLE 1 measurement probabilities of an anti- correlated entangledsystem (B1, B2) B1\B2 |0> |1> |0>  0% 50% |1> 50%  0%

TABLE 2 measurement probabilities of an uncorrelated system (B1, B2)B1\B2 |0> |1> |0> 25% 25% |1> 25% 25%

However, if Alice repeats the process of selectively entangling herqubits (A1 and A2) for each entanglement pair 76 of a set ofentanglement pairs (i.e., an entanglement set 80), Bob may statisticallydetermine whether his corresponding entanglement pairs 76 of hiscorresponding entanglement set 80 belong to a correlated distribution(e.g., consistent with Table 1) or an uncorrelated distribution (e.g.,consistent with Table 2).

Further, Bob may classify the correlated distributions as positivelycorrelated distributions (B1 and B2 are always measured in the samebasis state) or anti-correlated distributions (negatively correlateddistributions; B1 and B2 are always measured in opposite basis states,as shown in Table 1). If Alice entangles all entanglement pairs 76 ofone of her entanglement sets 80 such that every entanglement pair 76 ofBob's corresponding entanglement set 80 is in a positively correlateddistribution or an anti-correlated distribution, the classical bit ofdata Bob receives may have three values (i.e., the bit is a trit),corresponding to an uncorrelated distribution (random distribution), apositively correlated distribution, and an anti-correlated distribution.

The shared basis set for Alice's entanglement and Bob's measurement maybe the same, but does not need to be the same, for each correspondingentanglement pair 76. Alice and Bob may agree to use one basis set forsome corresponding entanglement-measurement operations and use anotherbasis set for other corresponding entanglement-measurement operations.Where Alice and Bob do change the basis set during communication, thechange may be periodic and/or may follow a pattern communicated betweenAlice and Bob.

The entanglement state of each of the entangled groups 72 may be thesame or may differ among entangled groups. The entanglement states ofthe entangled groups 72 corresponding to an entanglement pair 76, anentanglement set 80, and/or an entanglement queue 84 may be the same ordifferent (and/or the same or different type) within the entanglementpair 76, the entanglement set 80, and/or the entanglement queue 84.

When Alice selects to entangle each of her entanglement pairs 76 of herentanglement set 80, Alice may, but does not need to, entangle each ofthe entanglement pairs 76 in the same manner (i.e., imposing the sameentanglement state on each). Alice may entangle her entanglement pairs76 of an entanglement set 80 and/or an entanglement queue 84 into thesame or different (and/or the same or different type of) entanglementstate.

To determine the type of distribution (correlated or uncorrelated) ofthe entanglement pairs 76 of Bob's entanglement set 80, Bob may know,and/or receive information relating to, the entanglement state of eachof the entangled groups 72 corresponding to Bob's entanglement set 80.Additionally or alternatively, Bob may know, and/or receive informationindicating, that all of the entanglement states of the entangled groups72 corresponding to Bob's entanglement set 80 and/or to any of Bob'sentanglement pairs 76 are the same and/or have a defined pattern. Aliceand Bob may agree to a defined protocol and/or order of entanglementstates of the entangled groups before and/or during communication withthe entangled qubits. Additionally or alternatively, Bob may receive aprotocol and/or order of entanglement states of the entangled groups.

To determine the type of distribution (correlated or uncorrelated) ofthe entanglement pairs 76 of Bob's entanglement set 80, Bob may know,and/or receive information relating to, the possible entanglement stateof each of Alice's entanglement pairs 76 and/or the possibleentanglement state of each of Bob's entanglement pairs 76. Additionallyor alternatively, Bob may know, and/or receive information indicating,that all of the possible entanglement states of Alice's entanglementpairs 76 and/or Bob's entanglement pairs 76 are the same and/or have adefined pattern. For example, Bob may expect that, if Alice entangledher entanglement pairs 76, Bob's entanglement pairs 76 should be in agiven entanglement state, a given type of entanglement state, the sameentanglement state each time Alice entangles her correspondingentanglement pairs 76, and/or the same type of entanglement state eachtime Alice entangles her corresponding entanglement pairs 76. Alice andBob may agree to a defined protocol and/or order of entanglement statesof the entanglement pairs 76 before and/or during communication with theentangled qubits 70. Additionally or alternatively, Bob may receive,and/or Alice may send, a protocol of and/or an order of entanglementstates of the entanglement pairs 76.

The fidelity, or reliability, of the determination of the entanglementpair distribution increases with increasing numbers of entanglementpairs. The fidelity is the probability of correctly classifying anentangled state as entangled and a separable state as separable. Theprobability of misclassifying a separable state as an entangled state isthe probability that the separable state will be measured in a stateconsistent with an entangled state. Following the example of Tables 1and 2, a single entanglement pair in a separable state would be measuredin an apparently correlated state (|0> and |1>, or |1> and |0>) with anet 50% probability. The corresponding fidelity (the probability ofproper classification) is 50%. Hence, utilization of a singleentanglement pair 76 transfers no information (consistent with theno-communication theorem).

However, utilization of more than one entanglement pair 76 in anentanglement set 80 leads to a greater fidelity and, with sufficiententanglement pairs 76, the fidelity may be made arbitrarily close to100%. For example, the probability of misclassification of twoentanglement pairs is 25% (50% of 50%), with the corresponding fidelitybeing 75%. The probability of misclassification is 2^(−N), where N isthe number of entanglement pairs 76 in the entanglement set 80. Thecorresponding fidelity is 1-2^(−N). The number of entanglement pairs 76in an entanglement set 80 may be selected for a threshold fidelity(e.g., greater than 50%, greater than 75%, or higher). For example, thenumber of entanglement pairs 76 may be at least 2, at least 8, at least16, at least 24, at least 32, or at least 36.

A single classical bit of data (e.g., 0 or 1) may be sent by Alice byselectively entangling all of the entanglement pairs 76 of one ofAlice's entanglement sets 80 (Alice's selected entanglement set). Thevalue of the classical bit as received by Bob would correspond todetermining a correlated distribution or an uncorrelated distributionamong the corresponding entanglement pairs 76 of Bob's correspondingentanglement set 80. Alice may entangle each entanglement pair 76 of herselected entanglement set 80 to entangle every entanglement pair 76 ofBob's corresponding entanglement set 80 and thereby to produce acorrelated distribution of entanglement pairs 76 in Bob's correspondingentanglement set 80. For example, Alice may perform a Bell-statemeasurement on each entanglement pair 76 of her selected entanglementset 80. Alice may entangle less than all of the entanglement pairs 76 ofher selected entanglement set 80 to entangle less than all entanglementpairs 76 of Bob's corresponding entanglement set 80 and thereby toproduce an uncorrelated distribution of entanglement pairs 76 in Bob'scorresponding entanglement set 80. For example, Alice may refrain fromperforming a Bell-state measurement on at least one, optionally all, ofthe entanglement pairs 76 of her selected entanglement set 80. Alice mayrefrain from performing a Bell-state measurement by, e.g., doing nothingwith the entanglement pair(s) or performing a separable-statemeasurement with the entanglement pair(s).

Before and/or during communication, Alice and Bob may desire tosynchronize their mutual time so that they may coordinate sending andreceiving of classical bits as disclosed. One method to synchronize themutual time is to send a bitstream of classical bits that correspond tocorrelated distributions of entanglement pairs 76 in Bob's entanglementsets 80. The bitstream of classical bits may be sent by Alicesubstantially simultaneously at a predetermined time of the sender(Alice). Bob may begin to check his entanglement queue 84 ofentanglement sets 80 that correspond to Alice's classical bits beforethe predetermined time (as perceived by Bob). Bob may check hisentanglement sets 80 one at a time, offset by a predeterminedinterval(s). The initial entanglement sets 80 measured by Bob would havean uncorrelated distribution of entanglement pairs 76 because Bob wouldbe measuring before Alice would be able to impress any entanglement onher corresponding entanglement pairs 76. Bob would observe a correlateddistribution in the first determination of the distribution after Alicesent the bitstream. Alice's bitstream is sent substantiallysimultaneously when all of the classical bits of the bitstream are sentfaster than the interval(s) between Bob's determinations of thedistributions of entanglement sets. Alice and Bob may utilize thismethod to synchronize their mutual time at different times (e.g., once aday) and/or with different intervals (e.g., one minute for coarsesynchronization, one millisecond for fine synchronization).

The communication protocol may rely on polling for a classical bit thatcorresponds to a correlated distribution. For this example, a classicalbit that corresponds to a correlated distribution will be referred to asa logical 1 and a classical bit that corresponds to an uncorrelateddistribution will be referred to as a logical 0. Polling includessending and receiving a classical bit at one or more predetermined times(e.g., periodically sending and receiving). Alice and Bob coordinatesuch that Alice sends the classical bit (i.e., selectively entangles herentanglement set 80) before Bob receives the classical bit (i.e.,determines the distribution of entanglement pairs 76 in Bob'scorresponding entanglement set 80). The rate and/or pattern of pollingmay be changed while communicating.

By utilizing a polling scheme, qubits 70 and entanglement pairs 76 maybe conserved for another message. As disclosed, each qubit 70 only maybe utilized once. After measurement, the qubits 70 are no longerentangled and no longer in a superposition state. The communicationdevices 12 may have a limited supply and/or may have a slowlyreplenished supply of qubits 70 and entanglement pairs 76. Hence,conservation of qubits 70 and entanglement pairs 76 may be desirable.

When Alice sends a logical 1 and Bob receives the logical 1, Alice andBob may agree to transmit a message that comprises a message payload andan optional length field. The message comprises a bitstream of classicalbits. The message may begin with the optional length field, whichencodes the length of the message and/or the message payload. Themessage payload includes a bitstream of classical bits that encode thedesired message.

Other message protocols may include sending and receiving a bitstream ofclassical bits at one or more predetermined times. The bitstream mayhave a predefined length or the bitstream may include a length field.The bitstream also may include a message payload.

Examples of inventive subject matter according to the present disclosureare described in the following enumerated paragraphs.

A1. A method of communicating a classical bit, the method comprising:

forming an entanglement set of at least two entanglement pairs and acorresponding entanglement set of at least two correspondingentanglement pairs, wherein each entanglement pair and correspondingentanglement pair are formed together by:

-   -   forming a first entanglement group by entangling a first qubit        and a second qubit;    -   forming a second entanglement group by entangling a third qubit        and a fourth qubit;    -   locating the first qubit and the third qubit in a first location        to form the entanglement pair; and    -   locating the second qubit and the fourth qubit in a second        location to form the corresponding entanglement pair.

A2. The method of paragraph A1, further comprising:

sending a classical bit from the first location to the second locationby one of

-   -   (a) entangling each entanglement pair of the entanglement set to        produce a correlated distribution in the corresponding        entanglement set in which every corresponding entanglement pair        of the corresponding entanglement set is entangled, or    -   (b) entangling less than all of the entanglement pairs of the        entanglement set to produce an uncorrelated distribution in the        corresponding entanglement set in which less than all        corresponding entanglement pairs of the corresponding        entanglement set are entangled;

wherein the classical bit has one of two binary values that correspondto the correlated distribution and the uncorrelated distribution.

A2.1. The method of paragraph A2, wherein the (a) entangling includesperforming a joint entanglement measurement on each entanglement pair ofthe entanglement set, and optionally wherein the joint entanglementmeasurement is at least one of a Bell-state measurement or a completeBell-state measurement.

A2.2. The method of any of paragraphs A2-A2.1, wherein the (a)entangling includes projecting all entanglement pairs of theentanglement set onto projected entangled states.

A2.2.1. The method of paragraph A2.2, wherein each projected entangledstate is an identical entangled state.

A2.2.2. The method of any of paragraphs A2.2-A2.2.1, wherein theprojected entangled states of the entanglement pairs include a firstentangled state and a second entangled state that is different from thefirst entangled state.

A2.2.3. The method of any of paragraphs A2.2-A2.2.2, wherein all of theprojected entangled states are one of all positively-correlatedentangled states or all anti-correlated entangled states.

A2.2.4. The method of any of paragraphs A2.2-A2.2.3, wherein eachprojected entangled state independently is one of apositively-correlated entangled state or an anti-correlated entangledstate.

A2.2.5. The method of any of paragraphs A2.2-A2.2.4, wherein theprojected entangled state is a Bell state.

A2.3. The method of any of paragraphs A2-A2.2.5, wherein the (b)entangling includes performing a separable-state measurement on at leastone, optionally each, of the entanglement pairs of the entanglement set.

A2.4. The method of any of paragraphs A2-A2.3, wherein the (b)entangling includes projecting at least one, optionally each, of theentanglement pairs of the entanglement set onto a separable state.

A2.5. The method of any of paragraphs A2-A2.4, further comprisingrepeating, optionally periodically repeating, the forming anentanglement set and corresponding entanglement set, and the sending aclassical bit, optionally to produce a digital message with a bitstreamof classical bits.

A2.5.1. The method of paragraph A2.5, wherein the repeating includesforming an entanglement queue of entanglement sets in the first locationand a corresponding entanglement queue of corresponding entanglementsets in the second location.

A2.5.1.1. The method of paragraph A2.5.1, wherein the entanglement queueand the corresponding entanglement queue have an order, wherein thesending a classical bit is performed with each entanglement set of theentanglement queue in the order of the entanglement queue.

A2.5.1.2. The method of any of paragraphs A2.5.1-A2.5.1.1, wherein eachentanglement set of the entanglement queue has a given number ofentanglement pairs and wherein each corresponding entanglement set ofthe corresponding entanglement queue has a number of correspondingentanglement pairs that is equal to the given number.

A2.5.1.3. The method of any of paragraphs A2.5.1-A2.5.1.1, wherein theentanglement queue includes a first entanglement set with a first numberof entanglement pairs and a second entanglement set with a second numberof entanglement pairs, wherein the corresponding entanglement queueincludes a first corresponding entanglement set with the first number ofentanglement pairs and a second corresponding entanglement set with thesecond number of entanglement pairs, and wherein the first number isdifferent than the second number.

A2.5.2. The method of any of paragraphs A2.5-A2.5.1.3, wherein thedigital message has a predetermined length of bits.

A2.5.3. The method of any of paragraphs A2.5-A2.5.2, wherein the digitalmessage includes a field indicating a length of the digital message.

A2.5.4. The method of any of paragraphs A2.5-A2.5.3, wherein the digitalmessage includes a field indicating a time until a future transmission.

A2.5.5. The method of any of paragraphs A2.5-A2.5.4, wherein the digitalmessage includes a field indicating a fidelity of a future transmission,optionally wherein the fidelity is related to a number of entanglementpairs in a queued entanglement set for a future transmission.

A2.5.6. The method of any of paragraphs A2.5-A2.5.5, wherein the methodincludes sending a first classical bit with a binary value correspondingto the correlated distribution before the repeating to produce a digitalmessage with a bitstream of classical bits.

A2.5.7. The method of any of paragraphs A2.5-A2.5.6, wherein therepeating the sending includes sending classical bits at predeterminedtimes.

A3. The method of any of paragraphs A1-A2.5.7, further comprising:

receiving a classical bit from the first location at the second locationby one of

-   -   (a) determining that each corresponding entanglement pair of the        corresponding entanglement set is in a possible entangled state        to identify a correlated distribution in the corresponding        entanglement set, or    -   (b) determining that at least one, optionally each, of the        corresponding entanglement pairs of the corresponding        entanglement set is in a separable state to identify an        uncorrelated distribution in the corresponding entanglement set;

wherein the classical bit has one of two binary values that correspondto the correlated distribution and the uncorrelated distribution.

A3.1. The method of paragraph A3, wherein the receiving includesdetermining a probability that all corresponding entanglement pairs ofthe corresponding entanglement set are in entangled states, optionallywherein the correlated distribution corresponds to the probability beinggreater than a predetermined threshold and the uncorrelated distributioncorresponds to the probability being less than or equal to thepredetermined threshold.

A3.1.1. The method of paragraph A3.1, wherein the predeterminedthreshold is one of 50%, 75%, greater than 50%, or greater than 75%.

A3.1.2. The method of any of paragraphs A3.1-A3.1.1, wherein thepredetermined threshold is 1-2^(−(N−1)), wherein N is a number ofcorresponding entanglement pairs in the corresponding entanglement set.

A3.2. The method of any of paragraphs A3-A3.1.2, wherein the receivingincludes performing a separable-state measurement on at least one,optionally each, corresponding entanglement pair of the correspondingentanglement set.

A3.3. The method of any of paragraphs A3-A3.2, wherein the receivingincludes performing a separable-state measurement on correspondingentanglement pairs of the corresponding entanglement set until at leastone of (a) all corresponding entanglement pairs of the correspondingentanglement set have been measured or (b) one correspondingentanglement pair of the corresponding entanglement set is measured inthe separable state.

A3.4. The method of any of paragraphs A3-A3.3, when also depending fromparagraph A2, wherein the receiving is after the sending.

A3.5. The method of any of paragraphs A3-A3.4, further comprisingrepeating, optionally periodically repeating, the forming anentanglement set and corresponding entanglement set, and the receiving aclassical bit, optionally to receive a digital message including abitstream of classical bits.

A3.5.1. The method of paragraph A3.5, wherein the repeating includesforming an entanglement queue of entanglement sets in the first locationand a corresponding entanglement queue of corresponding entanglementsets in the second location.

A3.5.1.1. The method of paragraph A3.5.1, wherein the entanglement queueand the corresponding entanglement queue have an order, wherein thereceiving a classical bit is performed with each correspondingentanglement set of the corresponding entanglement queue in the order ofthe corresponding entanglement queue.

A3.5.1.2. The method of any of paragraphs A3.5.1-A3.5.1.1, wherein eachentanglement set of the entanglement queue has a given number ofentanglement pairs and wherein each corresponding entanglement set ofthe corresponding entanglement queue has a number of correspondingentanglement pairs that is equal to the given number.

A3.5.1.3. The method of any of paragraphs A3.5.1-A3.5.1.1, wherein theentanglement queue includes a first entanglement set with a first numberof entanglement pairs and a second entanglement set with a second numberof entanglement pairs, wherein the corresponding entanglement queueincludes a first corresponding entanglement set with the first number ofentanglement pairs and a second corresponding entanglement set with thesecond number of entanglement pairs, and wherein the first number isdifferent than the second number.

A3.5.2. The method of any of paragraphs A3.5-A3.5.1.3, wherein therepeating the receiving includes receiving classical bits atpredetermined times.

A4. The method of any of paragraphs A1-A3.5.2, wherein the first qubit,the second qubit, the third qubit, and/or the fourth qubit is a quantumsystem that includes at least one of a boson, a fermion, a photon, anelectron, an ion, an atom, a molecule, a quasiparticle, an exciton, aplasmon, or a quantum dot.

A5. The method of any of paragraphs A1-A4, wherein the first qubit, thesecond qubit, the third qubit, and/or the fourth qubit is based on atleast one of polarization of a photon, orbital angular momentum of aphoton, presence of a photon, spin of an electron, presence of anelectron, or a two-state parameter of a quantum system.

A6. The method of any of paragraphs A1-A5, wherein the forming the firstentanglement group includes at least one of (a) generating the firstqubit and the second qubit in a first entangled state or (b) projectingthe first qubit and the second qubit onto the first entangled state.

A6.1. The method of paragraph A6, when also depending from paragraph A2,wherein the (a) entangling includes projecting each entanglement pair ofthe entanglement set onto the first entangled state.

A7. The method of any of paragraphs A1-A6.1, wherein the forming thesecond entanglement group includes at least one of (a) generating thethird qubit and the fourth qubit in a second entangled state or (b)projecting the third qubit and the fourth qubit onto the secondentangled state.

A7.1. The method of paragraph A7, when also depending from paragraph A6,wherein the first entangled state is identical to the second entangledstate.

A7.2. The method of any of paragraphs A7-A7.1, when also depending fromparagraph A2, wherein the (a) entangling includes projecting eachentanglement pair of the entanglement set onto the second entangledstate.

A8. The method of any of paragraphs A1-A7.2, wherein the forming theentanglement set and the corresponding entanglement set includes formingthe entanglement set with a given number of entanglement pairs and thecorresponding entanglement set with a number of correspondingentanglement pairs that is equal to the given number, wherein the givennumber is at least 8, at least 16, at least 24, at least 32, or at least36.

A9. The method of any of paragraphs A1-A8, when also depending fromparagraph A3, further comprising:

repeating the forming an entanglement set and a correspondingentanglement set to form an entanglement queue of entanglement sets inthe first location and a corresponding entanglement queue ofcorresponding entanglement sets in the second location;

polling for a classical bit corresponding to the correlated distributionby repeating the receiving at a sequence of receive times;

sending from the first location to the second location, at apredetermined send time during the polling, a bitstream of classicalbits corresponding to the correlated distribution by entangling eachentanglement pair of each entanglement set of the entanglement queue toproduce the correlated distribution in the corresponding entanglementsets of the corresponding entanglement queue in which everycorresponding entanglement pair of every corresponding entanglement setis entangled; and

determining a time offset between the first location and the secondlocation by comparing the predetermined send time with the receive timethat corresponds to first receiving a classical bit corresponding to thecorrelated distribution.

A10. The method of any of paragraphs A1-A9, wherein the method is amethod of time synchronization.

A11. The method of any of paragraphs A1-A10, wherein the pollingincludes repeating the receiving for each corresponding entanglement setin the corresponding entanglement queue.

A12. The method of any of paragraphs A1-A11, wherein the pollingincludes repeating until receiving a classical bit corresponding to thecorrelated distribution.

A13. The method of any of paragraphs A1-A12, further comprisingadjusting a local time at the second location based upon the timeoffset.

B1. A method of digitally communicating between a sending device and areceiving device, wherein each of the sending device and the receivingdevice includes an entanglement set of entanglement pairs of qubits,wherein each qubit of the sending device is entangled with acorresponding qubit of the receiving device, the method comprising:

sending a classical bit from the sending device to the receiving deviceby one of

-   -   (a) entangling each entanglement pair of the entanglement set of        the sending device to produce a correlated distribution in the        entanglement set of the sending device in which every        entanglement pair of the entanglement set of the receiving        device is entangled, or    -   (b) entangling less than all of the entanglement pairs of the        entanglement set of the sending device to produce an        uncorrelated distribution in the entanglement set of the        receiving device in which less than all entanglement pairs of        the entanglement set of the receiving device are entangled;

wherein the classical bit has one of two binary values that correspondto the correlated distribution and the uncorrelated distribution.

B2. The method of paragraph B1, wherein the (a) entangling includesperforming a joint entanglement measurement on each entanglement pair ofthe entanglement set of the sending device, and optionally wherein thejoint entanglement measurement is at least one of a Bell-statemeasurement or a complete Bell-state measurement.

B3. The method of any of paragraphs B1-B2, wherein the (a) entanglingincludes projecting each entanglement pair of the entanglement set ofthe sending device onto a projected entangled state.

B3.1. The method of paragraph B3, wherein each projected entangled stateis an identical entangled state.

B3.2. The method of any of paragraphs B3-B3.1, wherein the projectedentangled states include a first entangled state and a second entangledstate that is different from the first entangled state.

B3.3. The method of any of paragraphs B3-B3.2, wherein all of theprojected entangled states are one of all positively-correlatedentangled states or all anti-correlated entangled states.

B3.4. The method of any of paragraphs B3-B3.3, wherein each projectedentangled state independently is one of a positively-correlatedentangled state or an anti-correlated entangled state.

B3.5. The method of any of paragraphs B3-B3.4, wherein the projectedentangled state is a Bell state.

B4. The method of any of paragraphs B1-B3.5, wherein the (b) entanglingincludes performing a separable-state measurement on at least one,optionally each, of the entanglement pairs of the entanglement set ofthe sending device.

B5. The method of any of paragraphs B1-B4, wherein the (b) entanglingincludes projecting at least one, optionally each, of the entanglementpairs of the entanglement set of the sending device onto a separablestate.

B6. The method of any of paragraphs B1-B5, further comprising repeating,optionally periodically repeating, the sending to produce a digitalmessage with a bitstream of classical bits.

B6.1. The method of paragraph B6, wherein each of the sending device andthe receiving device includes an entanglement queue of entanglementsets, wherein the entanglement queue of the sending device and theentanglement queue of the receiving device have a common order ofentanglement sets, wherein repeating includes performing the sending foreach entanglement set of the entanglement queue of the sending device inthe common order.

B6.1.1. The method of paragraph B6.1, wherein each entanglement set ofthe entanglement queue of the sending device has a given number ofentanglement pairs and wherein each entanglement set of the entanglementqueue of the receiving device has the given number of entanglementpairs.

B6.1.2. The method of paragraph B6.1, wherein the entanglement queue ofthe sending device includes a first entanglement set with a first numberof entanglement pairs and a second entanglement set with a second numberof entanglement pairs, wherein the entanglement queue of the receivingdevice includes a first entanglement set with the first number ofentanglement pairs and a second entanglement set with the second numberof entanglement pairs, and wherein the first number is different thanthe second number.

B6.2. The method of any of paragraphs B6-B6.1.2, wherein the digitalmessage has a predetermined length of bits.

B6.3. The method of any of paragraphs B6-B6.2, wherein the digitalmessage includes a field indicating a length of the digital message.

B6.4. The method of any of paragraphs B6-B6.3, wherein the digitalmessage includes a field indicating a time until a future transmission.

B6.5. The method of any of paragraphs B6-B6.4, wherein the digitalmessage includes a field indicating a fidelity of a future transmission,optionally wherein the fidelity is related to a number of entanglementpairs in a queued entanglement set for a future transmission.

B6.6. The method of any of paragraphs B6-B6.5, wherein the methodincludes sending a first classical bit with a binary value correspondingto the correlated distribution before the repeating to produce a digitalmessage with a bitstream of classical bits.

B6.7. The method of any of paragraphs B6-B6.6, wherein the repeating thesending includes sending classical bits at predetermined times.

B7. The method of any of paragraphs B1-B6.7, wherein each qubit and/oreach corresponding qubit is a quantum system that includes at least oneof a boson, a fermion, a photon, an electron, an ion, an atom, amolecule, a quasiparticle, an exciton, a plasmon, or a quantum dot.

B8. The method of any of paragraphs B1-B7, wherein each qubit and/oreach corresponding qubit is based on at least one of polarization of aphoton, orbital angular momentum of a photon, presence of a photon, spinof an electron, presence of an electron, or a two-state parameter of aquantum system.

B9. The method of any of paragraphs B1-B8, wherein the entanglement setof the sending device and the entanglement set of the receiving deviceeach include at least 2, at least 8, at least 16, at least 24, at least32, or at least 36 entanglement pairs.

B10. The method of any of paragraphs B1-B9, wherein each qubit of thesending device and corresponding qubit of the receiving device togetherform an entangled group, and wherein each entangled group is in anidentical entangled state.

B10.1. The method of paragraph B10, wherein the (a) entangling includesprojecting each entanglement pair of the entanglement set of the sendingdevice onto the identical entangled state.

B11. The method of any of paragraphs B1-B10.1, wherein each qubit of thesending device and corresponding qubit of the receiving device togetherform an entangled group, and wherein each entangled group is in amaximally entangled state.

C1. A method of digitally communicating between a sending device and areceiving device, wherein each of the sending device and the receivingdevice includes an entanglement set of entanglement pairs of qubits,wherein each qubit of the sending device is entangled with acorresponding qubit of the receiving device, the method comprising:

receiving a classical bit at the receiving device from the sendingdevice by one of

-   -   (a) determining that each entanglement pair of the entanglement        set of the receiving device is in a possible entangled state to        identify a correlated distribution in the entanglement set of        the receiving device, or    -   (b) determining that at least one of the entanglement pairs of        the entanglement set of the receiving device is in a separable        state to identify an uncorrelated distribution in the        entanglement set of the receiving device;

wherein the classical bit has one of two binary values that correspondto the correlated distribution and the uncorrelated distribution.

C1.1. The method of paragraph C1, further comprising any of the methodsof any of paragraphs B1-B11.

C1.1.1. The method of paragraph C1.1, wherein a number of entanglementpairs in the entanglement set of the sending device equals a number ofentanglement pairs in the entanglement set of the receiving device.

C2. The method of any of paragraphs C1-C1.1.1, wherein the receivingincludes determining a probability that all entanglement pairs of theentanglement set of the receiving device are in entangled states,optionally wherein the correlated distribution corresponds to theprobability being greater than a predetermined threshold and theuncorrelated distribution corresponds to the probability being less thanor equal to the predetermined threshold.

C2.1. The method of paragraph C2, wherein the predetermined threshold isone of 50%, 75%, greater 50%, or greater than 75%.

C2.2. The method of any of paragraphs C2-C2.1, wherein the predeterminedthreshold is 1-2^(−(N−1)), wherein N is a number of entanglement pairsin the entanglement set of the receiving device, and optionally whereinN is at least 2, at least 8, at least 16, at least 24, at least 32, orat least 36.

C3. The method of any of paragraphs C1-C2.2, wherein the receivingincludes performing a separable-state measurement on at least one,optionally each, entanglement pair of the entanglement set of thereceiving device.

C4. The method of any of paragraphs C1-C3, wherein the receivingincludes performing a separable-state measurement on entanglement pairsof the entanglement set of the receiving device until at least one of(a) all entanglement pairs of the entanglement set of the receivingdevice have been measured or (b) one entanglement pair of theentanglement set of the receiving device is measured in the separablestate.

C5. The method of any of paragraphs C1-C4, when also depending fromparagraph C1.1, wherein the receiving is after the sending.

C6. The method of any of paragraphs C1-C5, further comprising repeating,optionally periodically repeating, the receiving to receive a digitalmessage with a bitstream of classical bits. C6.1. The method ofparagraph C6, wherein each of the sending device and the receivingdevice includes an entanglement queue of entanglement sets, wherein theentanglement queue of the sending device and the entanglement queue ofthe receiving device have a common order of entanglement sets, whereinthe repeating includes performing the receiving for each entanglementset of the entanglement queue of the receiving device in the commonorder.

C6.1.1. The method of paragraph C6.1, wherein each entanglement set ofthe entanglement queue of the sending device has a given number ofentanglement pairs and wherein each entanglement set of the entanglementqueue of the receiving device has the given number of entanglementpairs.

C6.1.2. The method of paragraph C6.1, wherein the entanglement queue ofthe sending device includes a first entanglement set with a first numberof entanglement pairs and a second entanglement set with a second numberof entanglement pairs, wherein the entanglement queue of the receivingdevice includes a first entanglement set with the first number ofentanglement pairs and a second entanglement set with the second numberof entanglement pairs, and wherein the first number is different thanthe second number.

C6.2. The method of any of paragraphs C6-C6.1.2, wherein the digitalmessage has a predetermined length of bits.

C6.3. The method of any of paragraphs C6-C6.2, wherein the digitalmessage includes a field indicating a length of the digital message.

C6.4. The method of any of paragraphs C6-C6.3, wherein the digitalmessage includes a field indicating a time until a future transmission.

C6.5. The method of any of paragraphs C6-C6.4, wherein the digitalmessage includes a field indicating a fidelity of a future transmission,optionally wherein the fidelity is related to a number of entanglementpairs in a queued entanglement set for a future transmission.

C6.6. The method of any of paragraphs C6-C6.5, wherein the repeating thereceiving includes receiving classical bits at predetermined times.

C7. The method of any of paragraphs C1-C6.6, wherein each qubit and/oreach corresponding qubit is a quantum system that includes at least oneof a boson, a fermion, a photon, an electron, an ion, an atom, amolecule, a quasiparticle, an exciton, a plasmon, or a quantum dot.

C8. The method of any of paragraphs C1-C7, wherein each qubit and/oreach corresponding qubit is based on at least one of polarization of aphoton, orbital angular momentum of a photon, presence of a photon, spinof an electron, presence of an electron, or a two-state parameter of aquantum system.

C9. The method of any of paragraphs C1-C8, wherein the entanglement setof the sending device and the entanglement set of the receiving deviceeach include at least 2, at least 8, at least 16, at least 24, at least32, or at least 36 entanglement pairs.

C10. The method of any of paragraphs C1-C9, wherein each qubit of thesending device and corresponding qubit of the receiving device togetherform an entangled group, and wherein each entangled group is in anidentical entangled state.

C11. The method of any of paragraphs C1-C10, wherein each qubit of thesending device and corresponding qubit of the receiving device togetherform an entangled group, and wherein each entangled group is in amaximally entangled state.

D1. A method of time synchronization between a sending device at asending location and a receiving device at a receiving location, whereineach of the sending device and the receiving device includes anentanglement queue of entanglement sets of entanglement pairs of qubits,wherein each qubit of the sending device is entangled with acorresponding qubit of the receiving device, the method comprising:

polling by the receiving device for a marker classical bit correspondingto a correlated distribution by sequentially checking the entanglementsets of the entanglement queue of the receiving device at least untilidentifying the marker classical bit, wherein, for each entanglement setof the entanglement queue of the receiving device that is checked, thechecking includes one of

-   -   (a) determining that each entanglement pair of the entanglement        set checked is in a possible entangled state to identify the        correlated distribution in the entanglement set checked and to        identify the marker classical bit, or    -   (b) determining that at least one, optionally each, of the        entanglement pairs of the entanglement set checked is in a        separable state to identify an uncorrelated distribution in the        entanglement set checked;

sending from the sending device to the receiving device, at apredetermined local send time during the polling, a bitstream ofclassical bits, each classical bit corresponding to the correlateddistribution in one of the entanglement sets of the entanglement queueof the sending device, by entangling each entanglement pair of eachentanglement set of the entanglement queue of the sending device toproduce the correlated distribution in each of the entanglement sets ofthe entanglement queue of the receiving device; and

determining a time offset between the sending location and the receivinglocation by comparing the local send time with a local receive time thatcorresponds to first receiving the marker classical bit at the receivingdevice.

D2. The method of paragraph D1, further comprising determining the localreceive time that corresponds to first receiving the marker classicalbit at the receiving device.

D3. The method of any of paragraphs D1-D2, further comprising adjustinga local time of the receiving device based upon the time offset.

D4. The method of any of paragraphs D1-D3, wherein the polling includessequentially checking all of the entanglement sets of the entanglementqueue.

D5. The method of any of paragraphs D1-D4, wherein the sending includessending the bitstream substantially simultaneously.

D6. The method of any of paragraphs D1-D5, wherein the polling includeschecking the entanglement sets of the entanglement queue of thereceiving device one at a time, offset by a predetermined interval,optionally wherein the interval is at least 1 millisecond, at least 1second, at least 1 minute, less than 1 hour, and/or less than 1 minute.

D7. The method of any of paragraphs D1-D6, wherein each qubit and/oreach corresponding qubit is a quantum system that includes at least oneof a boson, a fermion, a photon, an electron, an ion, an atom, amolecule, a quasiparticle, an exciton, a plasmon, or a quantum dot.

D8. The method of any of paragraphs D1-D7, wherein each qubit and/oreach corresponding qubit is based on at least one of polarization of aphoton, orbital angular momentum of a photon, presence of a photon, spinof an electron, presence of an electron, or a two-state parameter of aquantum system.

D9. The method of any of paragraphs D1-D8, wherein each of theentanglement sets of the sending device and each of the entanglementsets of the receiving device each include at least 2, at least 8, atleast 16, at least 24, at least 32, or at least 36 entanglement pairs.

D10. The method of any of paragraphs D1-D9, wherein each qubit of thesending device and corresponding qubit of the receiving device togetherform an entangled group, and wherein each entangled group is in anidentical entangled state.

D10.1. The method of paragraph D10, wherein the entangling eachentanglement pair of each entanglement set of the entanglement queue ofthe sending device includes projecting each entanglement pair of eachentanglement set of the entanglement queue of the sending device ontothe identical entangled state.

D11. The method of any of paragraphs D1-D10.1, wherein each qubit of thesending device and corresponding qubit of the receiving device togetherform an entangled group, and wherein each entangled group is in amaximally entangled state.

D12. The method of any of paragraphs D1-D11, further comprising themethod of any of paragraphs A1-A13, B1-B11, and/or C1-C11.

E1. A sending device for communicating with a receiving devicecomprising:

an entanglement queue of entanglement sets of entanglement pairs ofqubits, wherein each qubit of the sending device is entangled with acorresponding qubit of the receiving device;

wherein the sending device is configured to send a digital message tothe receiving device by encoding a plurality of classical bits of datainto the entanglement sets of the sending device, wherein each classicalbit is encoded by one entanglement set of the entanglement queue, andwherein each classical bit is encoded as one of

-   -   (a) a correlated distribution of entanglement pairs in the one        entanglement set formed by entangling each entanglement pair of        the one entanglement set, or    -   (b) an uncorrelated distribution of entanglement pairs in the        one entanglement set formed by entangling less than all of the        entanglement pairs of the one entanglement set.

E2. The sending device of paragraph E1, wherein the sending device isconfigured, for each entanglement set of the entanglement queue, toselectively entangle all of the entanglement pairs of the entanglementset to encode the classical bit.

E3. The sending device of any of paragraphs E1-E2, wherein the sendingdevice is configured to perform any of the methods of paragraphs A1-A13,B1-B11, and/or D1-D12.

F1. A receiving device for receiving communication from a sending devicecomprising:

an entanglement queue of entanglement sets of entanglement pairs ofqubits, wherein each qubit of the receiving device is entangled with acorresponding qubit of the sending device;

wherein the receiving device is configured to receive a digital messagefrom the sending device by decoding a plurality of classical bits ofdata from the entanglement sets of the receiving device, wherein eachclassical bit is decoded from one entanglement set of the entanglementqueue, and wherein each classical bit is decoded by one of

-   -   (a) determining that each entanglement pair of the one        entanglement set is in a possible entangled state to identify a        correlated distribution in the one entanglement set and to        assign a first binary value to the classical bit, or    -   (b) determining that at least one of the entanglement pairs of        the one entanglement set is in a separable state to identify an        uncorrelated distribution in the one entanglement set and to        assign a second binary value to the classical bit.

F2. The receiving device of paragraph F1, wherein the receiving deviceis configured to perform any of the methods of paragraphs A1-A13,C1-C11, and/or D1-D12.

G1. A communication system comprising:

at least one sending device of any of paragraphs E1-E3; and

at least one receiving device of any of paragraphs F1-F2.

As used herein, the terms “selective” and “selectively,” when modifyingan action, movement, configuration, or other activity of one or morecomponents or characteristics of an apparatus, mean that the specificaction, movement, configuration, or other activity is a direct orindirect result of user manipulation of an aspect of, or one or morecomponents of, the apparatus.

As used herein, the terms “adapted” and “configured” mean that theelement, component, or other subject matter is designed and/or intendedto perform a given function. Thus, the use of the terms “adapted” and“configured” should not be construed to mean that a given element,component, or other subject matter is simply “capable of” performing agiven function but that the element, component, and/or other subjectmatter is specifically selected, created, implemented, utilized,programmed, and/or designed for the purpose of performing the function.It is also within the scope of the present disclosure that elements,components, and/or other recited subject matter that is recited as beingadapted to perform a particular function may additionally oralternatively be described as being configured to perform that function,and vice versa. Similarly, subject matter that is recited as beingconfigured to perform a particular function may additionally oralternatively be described as being operative to perform that function.Further, as used herein, the singular forms “a”, “an” and “the” may beintended to include the plural forms as well, unless the context clearlyindicates otherwise.

The various disclosed elements of systems and steps of methods disclosedherein are not required of all systems and methods according to thepresent disclosure, and the present disclosure includes all novel andnon-obvious combinations and subcombinations of the various elements andsteps disclosed herein. Moreover, any of the various elements and steps,or any combination of the various elements and/or steps, disclosedherein may define independent inventive subject matter that is separateand apart from the whole of a disclosed apparatus or method.Accordingly, such inventive subject matter is not required to beassociated with the specific systems and methods that are expresslydisclosed herein, and such inventive subject matter may find utility insystems and/or methods that are not expressly disclosed herein.

As used herein, the phrase, “for example,” the phrase, “as an example,”and/or simply the term “example,” when used with reference to one ormore components, features, details, structures, embodiments, and/ormethods according to the present disclosure, are intended to convey thatthe described component, feature, detail, structure, embodiment, and/ormethod is an illustrative, non-exclusive example of components,features, details, structures, embodiments, and/or methods according tothe present disclosure. Thus, the described component, feature, detail,structure, embodiment, and/or method is not intended to be limiting,required, or exclusive/exhaustive; and other components, features,details, structures, embodiments, and/or methods, including structurallyand/or functionally similar and/or equivalent components, features,details, structures, embodiments, and/or methods, are also within thescope of the present disclosure.

As used herein, the phrases “at least one of” and “one or more of,” inreference to a list of more than one entity, mean any one or more of theentities in the list of entities, and are not limited to at least one ofeach and every entity specifically listed within the list of entities.For example, “at least one of A and B” (or, equivalently, “at least oneof A or B,” or, equivalently, “at least one of A and/or B”) may refer toA alone, B alone, or the combination of A and B. As used herein, thephrase “one of . . . or . . . ” indicates an exclusive disjunctive list.For example, “one of A or B” may refer to either A alone or B alone, butnot the combination of A and B.

The invention claimed is:
 1. A method of digitally communicating betweena sending device and a receiving device, wherein each of the sendingdevice and the receiving device includes an entanglement set ofentanglement pairs of qubits, wherein each qubit of the sending deviceis entangled with a corresponding qubit of the receiving device, themethod comprising: sending a classical bit from the sending device tothe receiving device by one of (a) entangling each entanglement pair ofthe entanglement set of the sending device to produce a correlateddistribution in the entanglement set of the sending device in whichevery entanglement pair of the entanglement set of the receiving deviceis entangled, or (b) entangling less than all of the entanglement pairsof the entanglement set of the sending device to produce an uncorrelateddistribution in the entanglement set of the receiving device in whichless than all entanglement pairs of the entanglement set of thereceiving device are entangled; and receiving the classical bit at thereceiving device from the sending device by one of (a) determining thateach entanglement pair of the entanglement set of the receiving deviceis in a possible entangled state to identify the correlated distributionin the entanglement set of the receiving device, or (b) determining thatat least one of the entanglement pairs of the entanglement set of thereceiving device is in a separable state to identify the uncorrelateddistribution in the entanglement set of the receiving device; whereinthe classical bit has one of two binary values that correspond to thecorrelated distribution and the uncorrelated distribution.
 2. The methodof claim 1, wherein the receiving is after the sending.
 3. The method ofclaim 1, wherein the (a) entangling includes performing a completeBell-state measurement on each entanglement pair of the entanglement setof the sending device.
 4. The method of claim 1, wherein the (a)entangling includes projecting each entanglement pair of theentanglement set of the sending device onto a projected entangled state,wherein each projected entangled state is an identical entangled state.5. The method of claim 1, wherein the (b) entangling includes projectingat least one of the entanglement pairs of the entanglement set of thesending device onto a separable state.
 6. The method of claim 1, furthercomprising repeating the sending to produce a digital message with abitstream of classical bits, and further comprising repeating thereceiving to receive the digital message with the bitstream of classicalbits.
 7. The method of claim 6, wherein each of the sending device andthe receiving device includes an entanglement queue of entanglementsets, wherein the entanglement queue of the sending device and theentanglement queue of the receiving device have a common order ofentanglement sets, wherein the repeating the sending includes performingthe sending for each entanglement set of the entanglement queue of thesending device in the common order, wherein the repeating the receivingincludes performing the receiving for each entanglement set of theentanglement queue of the receiving device in the common order.
 8. Themethod of claim 7, wherein the entanglement queue of the sending deviceincludes a first entanglement set with a first number of entanglementpairs and a second entanglement set with a second number of entanglementpairs, wherein the entanglement queue of the receiving device includes afirst entanglement set with the first number of entanglement pairs and asecond entanglement set with the second number of entanglement pairs,and wherein the first number is different than the second number.
 9. Themethod of claim 6, wherein the repeating the sending includes sendingclassical bits at predetermined times, and wherein the repeating thereceiving includes receiving classical bits at predetermined times. 10.The method of claim 1, wherein the entanglement set of the sendingdevice and the entanglement set of the receiving device each include atleast 32 entanglement pairs.
 11. The method of claim 1, wherein thereceiving includes determining a probability that all entanglement pairsof the entanglement set of the receiving device are in entangled states,wherein the correlated distribution corresponds to the probability beinggreater than a predetermined threshold and the uncorrelated distributioncorresponds to a probability being less than or equal to thepredetermined threshold.
 12. The method of claim 11, wherein thepredetermined threshold is 1-2^(−(N−1)), wherein N is a number ofentanglement pairs in the entanglement set of the receiving device. 13.The method of claim 1, wherein the receiving includes performing aseparable-state measurement on at least one entanglement pair of theentanglement set of the receiving device.
 14. The method of claim 1,wherein the receiving includes performing a separable-state measurementon entanglement pairs of the entanglement set of the receiving deviceuntil at least one of (a) all entanglement pairs of the entanglement setof the receiving device have been measured or (b) one entanglement pairof the entanglement set of the receiving device is measured in theseparable state.
 15. A method of time synchronization between a sendingdevice at a sending location and a receiving device at a receivinglocation, wherein each of the sending device and the receiving deviceincludes an entanglement queue of entanglement sets of entanglementpairs of qubits, wherein each qubit of the sending device is entangledwith a corresponding qubit of the receiving device, the methodcomprising: polling by the receiving device for a marker classical bitcorresponding to a correlated distribution by sequentially checking theentanglement sets of the entanglement queue of the receiving device atleast until identifying the marker classical bit, wherein, for eachentanglement set of the entanglement queue of the receiving device thatis checked, the checking includes one of (a) determining that eachentanglement pair of the entanglement set checked is in a possibleentangled state to identify the correlated distribution in theentanglement set checked and to identify the marker classical bit, or(b) determining that at least one of the entanglement pairs of theentanglement set checked is in a separable state to identify anuncorrelated distribution in the entanglement set checked; sending fromthe sending device to the receiving device, at a predetermined localsend time during the polling, a bitstream of classical bits, eachclassical bit corresponding to the correlated distribution in one of theentanglement sets of the entanglement queue of the sending device, byentangling each entanglement pair of each entanglement set of theentanglement queue of the sending device to produce the correlateddistribution in each of the entanglement sets of the entanglement queueof the receiving device; and determining a time offset between thesending location and the receiving location by comparing the local sendtime with a local receive time that corresponds to first receiving themarker classical bit at the receiving device.
 16. The method of claim15, further comprising adjusting a local time of the receiving devicebased upon the time offset.
 17. The method of claim 15, wherein thepolling includes sequentially checking all of the entanglement sets ofthe entanglement queue.
 18. The method of claim 15, wherein the sendingincludes sending the bitstream substantially simultaneously.
 19. Themethod of claim 15, wherein the polling includes checking theentanglement sets of the entanglement queue of the receiving device oneat a time, offset by a predetermined interval.
 20. The method of claim15, wherein each qubit of the sending device and corresponding qubit ofthe receiving device together is in an identical entangled state,wherein the entangling each entanglement pair of each entanglement setof the entanglement queue of the sending device includes projecting eachentanglement pair of each entanglement set of the entanglement queue ofthe sending device onto the identical entangled state.